The invention relates to a method of forming a set of constellations of points which are not equiprobable, which is intended to be used for transmitting data between a transmitter and a receiver, said method enabling to obtain for said set of constellations an average power that is lower than or equal to a fixed threshold.
The invention also relates to transmission/reception equipment implementing such a method (notably a modem), and a transmission system comprising such transmission/reception equipment.
The invention is notably applied to PCM-type (Pulse Code Modulation) modems and, more particularly, to the modems in accordance with Recommendation V.90 of the ITU (International Telecommunication Union).
In the following of the description, references are made to Recommendation V.90 to the prepublished version of September 1998.
Recommendation V.90 of the ITU employs a set of six constellations Ci for transmitting data between a PCM modem connected in digital fashion (called DPCM modem in the following of the description) and a PCM-type modem connected in analog fashion (called APCM modem in the following of the description). Each constellation Ci is formed by Mi points of a segment linear logarithmic compression law known by the name of A law or xcexc law.
In conformity with Recommendation V.90, the bits transmitted by a DPCM modem and received by an APCM modem are coded in groups of K bits to determine a point index Ki for each of the six constellations Ci. This coding operation is described in paragraph 5.4.3 of Recommendation V.90. It introduces different probabilities of occurrence for the points of the constellations Ci.
As indicated in paragraph 8.5.2 of Recommendation V.90, when a communication between a DPCM modem and an APCM modem is initialized, the DPCM modem sends to the APCM modem the maximum value of the average power of the set of constellations that will be used for the transmission. The APCM modem is then to form this set of constellations in order not to exceed this maximum average power.
Paragraph 8.5.2 also gives the expression P of the average power of a set of constellations Ci (i=0, . . . , 5) formed by points that are not equiprobable because of the coding operation described in paragraph 5.4.3:                     P        =                                            1              6                        ⁢                                          ∑                                  i                  =                  0                                5                            ⁢                                                P                  i                                ⁢                                  xe2x80x83                                ⁢                with                ⁢                                  xe2x80x83                                ⁢                                  P                  i                                                              =                                    1                              2                K                                      ⁢                                          ∑                                  j                  =                  0                                                                      M                    i                                    -                  1                                            ⁢                                                p                                      i                    ,                    j                                                  ·                                  n                                      i                    ,                    j                                                                                                          (        1        )            
where
pi,j is the square of the amplitude ai,j of the index point j in the constellation Ci,
ni,j represents the probability of occurrence of the index point j in the constellation i (the expression ni,j is given by Recommendation V.90 in paragraphs 8.5.2 and 5.4.3),
and K is the largest integer verifying       2    K    ≤            ∏              i        =        0            5        ⁢          xe2x80x83        ⁢                  M        i            .      
The calculation of the average power according to the expression (1) thus utilizes all the values of Mi. Consequently, it is necessary to form all the constellations Ci simultaneously by calculating the power P each time a point is added to one of the constellations Ci. This method is particularly complex.
It is an object of the invention to propose a simplified method of forming such a set of constellations.
Therefore, a method according to the invention and as described in the opening paragraph is characterized in that it comprises:
a first step consisting of forming a set of constellations based on approximate values of the powers of said constellations,
a second step consisting of verifying whether the average real power of the set of constellations obtained during the first step is lower than or equal to said threshold,
a third step consisting of readjusting said set once or several times, if necessary, by suppressing one or various points in one or various constellations, so that the real average power of said set is lower than or equal to the fixed threshold.
Thus, the invention enables to considerably reduce the number of calculations of the expression (1). Tests have shown that three calculations of the expression (1) were sufficient for forming a set of six constellations in conformity with Recommendation V.90 (one calculation in the second step and two calculations at the most in the third step).
Although the invention has been introduced within the scope of Recommendation V.90, it can be applied to all the cases where the points of the constellations are not equiprobable and thus the average power of the set of constellations assumes a complex form.